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Lights and outlets are often on different circuits. Bathroom outlets should be protected by a groundfault plug. The plug will have a test and reset button between the two plug ins at one outlet. It can protect meny outlets downstream so it may not be in the bathroom. It may be in the kitchen or nearby bedroom. Some have a green light when they are working and some have a red light when they are tripped. That would be my first guess, if not you may want to check breakers again, some don't look like they have tripped but you have to turn them fully off and back on again.
If non of that works we will be looking for a loose connection in a box somewhere in the house.

An open GFCI opens both the hot & neutral connection so if that's the case almost certainly there is a GFCI upstream somewhere that needs a reset.
It's otherwise unlikely that you'd lose both hot & neutral.

To test the hot, run an incand. lamp in a pigtail socket from a known good ground to the hot connection (should be the short slot) of the dead outlets. You'll need an extension cord as a test lead and you'll need clip leads. A plug inserted and then pulled 1/8" out of the sockets/outlets/receptacles will give you a good electrical connection to the socket's interior spring loaded blades.
Be careful and wear eye protection because if you short a hot line, little globs of molten copper or aluminum will be flying through the air.

To test the neutral, run an incand. lamp in a pigtail socket from a known good hot connection of some outlet to the neutral connection (should be the long slot) of the dead outlets.